Fixed Circle Theory for Multivalued Mappings With Bilateral Type Contractions

This paper investigates the fixed‐circle problem in metric spaces within the framework of multivalued mappings. We introduce three novel classes of bilateral contractions, namely, the Jaggi‐type bilateral, Dass‐Gupta type I bilateral, and Dass‐Gupta type II bilateral multivalued contractions, each specifically formulated to extend the fixed‐circle theory to the setting of multivalued mappings. By employing these generalized contractive conditions, we establish several fixed‐circle and fixed‐disc theorems and further extend our results to encompass integral‐type contractions. The theoretical findings are supported by illustrative examples that confirm the applicability and robustness of the proposed approach.